292 lines
7.3 KiB
C
292 lines
7.3 KiB
C
/* Implementation of the degree trignometric functions COSD, SIND, TAND.
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Copyright (C) 2020-2021 Free Software Foundation, Inc.
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Contributed by Steven G. Kargl <kargl@gcc.gnu.org>
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This file is part of the GNU Fortran runtime library (libgfortran).
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Libgfortran is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public
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License as published by the Free Software Foundation; either
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version 3 of the License, or (at your option) any later version.
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Libgfortran is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#include "libgfortran.h"
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#include <math.h>
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/* Body of library functions which are cannot be implemented on the current
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* platform because it lacks a capability, such as an underlying trigonometric
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* function (sin, cos, tan) or C99 floating-point function (fabs, fmod). */
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#define STRINGIFY_EXPAND(x) #x
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#define ERROR_RETURN(f, k, x) runtime_error (#f " is unavailable for" \
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" REAL(KIND=" STRINGIFY_EXPAND(k) ") because the system math library" \
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" lacks support for it"); \
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RETURN(x)
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/*
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For real x, let {x}_P or x_P be the closest representible number in the
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floating point representation which uses P binary bits of fractional
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precision (with IEEE rounding semantics).
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Similarly, let f_P(x) be shorthand for {f(x)}_P.
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Let ulp_P(x) be the unit of least precision for x: in other words the
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maximal value of |a_P - b_P| where a_P <= x <= b_P and a_P != b_P.
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Let x ~= y <-> | x - y | < ulp_P(x - y).
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Let deg(x) be the value of x radians in degrees.
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Values for each precision P were selected as follows.
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COSD_SMALL = 2**{-N} such that for all x <= COSD_SMALL:
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* cos(deg(x)) ~= 1, or equivalently:
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| 1 - cos(deg(x)) | < ulp_P(1).
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Unfortunately for SIND (and therefore TAND) a similar relation is only
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possible for REAL(4) and REAL(8). With REAL(10) and REAL(16), enough
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precision is available such that sin_P(x) != x_P for some x less than any
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value. (There are values where this equality holds, but the distance has
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inflection points.)
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For REAL(4) and REAL(8), we can select SIND_SMALL such that:
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* sin(deg(x)) ~= deg(x), or equivalently:
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| deg(x) - sin(deg(x)) | < ulp_P(deg(x)).
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*/
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#ifdef HAVE_GFC_REAL_4
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/* Build _gfortran_sind_r4, _gfortran_cosd_r4, and _gfortran_tand_r4 */
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#define KIND 4
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#define TINY 0x1.p-100 /* ~= 7.889e-31 */
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#define COSD_SMALL 0x1.p-7 /* = 7.8125e-3 */
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#define SIND_SMALL 0x1.p-5 /* = 3.125e-2 */
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#define COSD30 8.66025388e-01
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#define PIO180H 1.74560547e-02 /* high 12 bits. */
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#define PIO180L -2.76216747e-06 /* Next 24 bits. */
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#if defined(HAVE_FABSF) && defined(HAVE_FMODF) && defined(HAVE_COPYSIGNF)
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#ifdef HAVE_SINF
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#define ENABLE_SIND
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#endif
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#ifdef HAVE_COSF
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#define ENABLE_COSD
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#endif
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#ifdef HAVE_TANF
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#define ENABLE_TAND
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#endif
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#endif /* HAVE_FABSF && HAVE_FMODF && HAVE_COPYSIGNF */
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#ifdef GFC_REAL_4_INFINITY
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#define HAVE_INFINITY_KIND
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#endif
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#include "trigd_lib.inc"
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#undef KIND
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#undef TINY
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#undef COSD_SMALL
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#undef SIND_SMALL
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#undef COSD30
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#undef PIO180H
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#undef PIO180L
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#undef ENABLE_SIND
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#undef ENABLE_COSD
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#undef ENABLE_TAND
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#undef HAVE_INFINITY_KIND
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#endif /* HAVE_GFC_REAL_4... */
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#ifdef HAVE_GFC_REAL_8
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/* Build _gfortran_sind_r8, _gfortran_cosd_r8, and _gfortran_tand_r8 */
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#define KIND 8
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#define TINY 0x1.p-1000 /* ~= 9.33e-302 (min exp -1074) */
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#define COSD_SMALL 0x1.p-21 /* ~= 4.768e-7 */
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#define SIND_SMALL 0x1.p-19 /* ~= 9.537e-7 */
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#define COSD30 8.6602540378443860e-01
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#define PIO180H 1.7453283071517944e-02 /* high 21 bits. */
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#define PIO180L 9.4484253514332993e-09 /* Next 53 bits. */
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#if defined(HAVE_FABS) && defined(HAVE_FMOD) && defined(HAVE_COPYSIGN)
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#ifdef HAVE_SIN
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#define ENABLE_SIND
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#endif
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#ifdef HAVE_COS
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#define ENABLE_COSD
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#endif
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#ifdef HAVE_TAN
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#define ENABLE_TAND
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#endif
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#endif /* HAVE_FABS && HAVE_FMOD && HAVE_COPYSIGN */
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#ifdef GFC_REAL_8_INFINITY
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#define HAVE_INFINITY_KIND
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#endif
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#include "trigd_lib.inc"
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#undef KIND
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#undef TINY
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#undef COSD_SMALL
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#undef SIND_SMALL
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#undef COSD30
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#undef PIO180H
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#undef PIO180L
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#undef ENABLE_SIND
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#undef ENABLE_COSD
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#undef ENABLE_TAND
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#undef HAVE_INFINITY_KIND
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#endif /* HAVE_GFC_REAL_8... */
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#ifdef HAVE_GFC_REAL_10
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/* Build _gfortran_sind_r10, _gfortran_cosd_r10, and _gfortran_tand_r10 */
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#define KIND 10
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#define TINY 0x1.p-16400 /* ~= 1.28e-4937 (min exp -16494) */
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#define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */
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#undef SIND_SMALL /* not precise */
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#define COSD30 8.66025403784438646787e-01
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#define PIO180H 1.74532925229868851602e-02 /* high 32 bits */
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#define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */
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#if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL)
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#ifdef HAVE_SINL
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#define ENABLE_SIND
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#endif
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#ifdef HAVE_COSL
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#define ENABLE_COSD
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#endif
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#ifdef HAVE_TANL
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#define ENABLE_TAND
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#endif
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#endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */
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#ifdef GFC_REAL_10_INFINITY
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#define HAVE_INFINITY_KIND
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#endif
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#include "trigd_lib.inc"
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#undef KIND
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#undef TINY
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#undef COSD_SMALL
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#undef SIND_SMALL
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#undef COSD30
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#undef PIO180H
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#undef PIO180L
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#undef ENABLE_SIND
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#undef ENABLE_COSD
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#undef ENABLE_TAND
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#undef HAVE_INFINITY_KIND
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#endif /* HAVE_GFC_REAL_10 */
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#ifdef HAVE_GFC_REAL_16
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/* Build _gfortran_sind_r16, _gfortran_cosd_r16, and _gfortran_tand_r16 */
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#define KIND 16
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#define TINY 0x1.p-16400 /* ~= 1.28e-4937 */
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#undef SIND_SMALL /* not precise */
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#if GFC_REAL_16_DIGITS == 64
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/* 80 bit precision, use constants from REAL(10). */
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#define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */
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#define COSD30 8.66025403784438646787e-01
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#define PIO180H 1.74532925229868851602e-02 /* high 32 bits */
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#define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */
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#else
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/* Proper float128 precision. */
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#define COSD_SMALL 0x1.p-51 /* ~= 4.441e-16 */
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#define COSD30 8.66025403784438646763723170752936183e-01
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#define PIO180H 1.74532925199433197605003442731685936e-02
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#define PIO180L -2.39912634365882824665106671063098954e-17
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#endif
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#ifdef GFC_REAL_16_IS_LONG_DOUBLE
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#if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL)
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#ifdef HAVE_SINL
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#define ENABLE_SIND
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#endif
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#ifdef HAVE_COSL
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#define ENABLE_COSD
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#endif
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#ifdef HAVE_TANL
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#define ENABLE_TAND
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#endif
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#endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */
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#else
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/* libquadmath: HAVE_*Q are never defined. They must be available. */
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#define ENABLE_SIND
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#define ENABLE_COSD
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#define ENABLE_TAND
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#endif /* GFC_REAL_16_IS_LONG_DOUBLE */
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#ifdef GFC_REAL_16_INFINITY
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#define HAVE_INFINITY_KIND
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#endif
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#include "trigd_lib.inc"
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#undef KIND
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#undef TINY
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#undef COSD_SMALL
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#undef SIND_SMALL
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#undef COSD30
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#undef PIO180H
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#undef PIO180L
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#undef ENABLE_SIND
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#undef ENABLE_COSD
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#undef ENABLE_TAND
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#undef HAVE_INFINITY_KIND
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#endif /* HAVE_GFC_REAL_16 */
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